Physics 207 Lecture Notes / Study aids for Fall 2006
These "notes", if here, are supplementary to the lecture material
Monday, Sept 4 (Labor Day)
Wednesday, Sept 6 (Introduction to the
Class)
Web-based physics sites:
Link to lecture, Lecture 1, PowerPoint , Lecture 1,pdf
Friday, Sept 8: Introduction to honors
Monday, Sept 11 (Chapter 1: Physics and Measurement)
-
Link to lecture, Lecture 2, PowerPoint , Lecture 2(pdf)
- Mentioned the use of hand written "cheat sheets", one 8.5 X 11 inch sheet per exam
- Working together in groups is strongly encouraged
- Tutoring is available at the University Physics Society and/or GUTS (see general information page)
Monday, Sept 13 (Chapter 2: Motion in One Dimension)
Friday, Sept 15
Monday, Sept 18 (Chapter 3: Vectors)
- Vector
Addition (Shockwave plugin required) Basic graphical
look
at vector addition. Lets you see the "head" to "tail" addition. (Raman
Pfaff)
- Other
vector simulations
- Chapter 3-4 homework should be accessible now. Note:
There have been a few slight modifications from the original syllabus. Serway: Ch. 3: 8, 32, 36, 38, 54 and Ch. 4: 4, 6, 18, 34, 45, 55 using the WebAssign provided problems.
- Link to lecture, Lecture 4, PowerPoint , Lecture 4(pdf)
- Chapter 4: A physics demonstration (by F.K. Hwang): Frames
of reference
Wednesday, Sept 20 (Chapter 4: 2-D Motion)
Friday, Sept 22
Monday, Sept 25 (Chapter 5: Laws of Motion)
- Link to lecture, Lecture 6, PowerPoint , Lecture 6 (pdf)
- Homework 3 should be available now. There are some slight changes from the original syllabus.
- All students that are unable attend the first mid-term time slot should have communicated that information by now.
- Lecture 6 ended at kinetic friction. Static friction will be covered on Wednesday
Wednesday, Sept 27 (Chapter 6: Circular Motion)
- Link to lecture, Lecture 7, PowerPoint , Lecture 7 (pdf)
- Homeworks 3 (and from now on) due date will shift to 11:59 PM on Tuesday
- Lecture 7 ended with uniform circular motion with friction.
- Monday is a catch up day and we will look at non-uniform circular
motion, frames of reference and talk just a little bit about resistive
forces (i.e., drag).
- By Monday I will provide a link to a number of illustrative
cooperative learning questions. You may or may not have had them
in discussion. I will also create a non-graded exercise set on
Web-Assign for those wishing to run through a few more problem.
- There is a link to sample exams on the course information page.
The 2004 exam is typical of the level with the proviso that it
was a 60 minute exam.
Friday, Sept 29
Monday, Oct 2 (Catch-up Lecture)
- Cooperative learning questions are now posted at the library and can be accessed through my.wisc.edu
- Accelerated frames of reference: Observing in an
accelerated frame of reference creates the need to provide fictitious
forces. The box/train problem is more accessible if one uses an
inertial reference frame (a = 0). From this perspective the force
of friction on the box is towards the front of the train car (as it
should be) but the train car experiences a larger acceleration.
- Because of the supplemental 3a homework set students, I will
allow for substitutions by either 5.26 or 6.36 using the
WebAssign values. The handing of work is to make sure you are keeping
up.
- Link to the lecture, Lecture 8, PowerPoint , Lecture 8 (pdf)
Wednesday, Oct 4 (Review)
- Midterm I in Rm. 105 and 113 in Psychology, McBurney students go to Rm. 5310 Chamberlin Hall (on Thursday, Oct. 5)
- Exam lasts from 7:15 PM to 8:45 PM.
Bring a basic scientific calculator (up to a TI-84), an 8.5 x 11
in sheet of notes. We can provide blank paper for scratch work
but only work on the exam sheets itself will be graded.
- Link to the lecture, Lecture 9, PowerPoint , Lecture 9 (pdf)
- Slide
with friction notes
Friday, Oct 6
Monday, Oct 9 (Chapter 7: Work and Energy)
- Link to the lecture, Lecture 10, PowerPoint , Lecture 10 (pdf)
- Midterm 1 has been graded and will be returned during the
next discussion section. Exam statistics and a conservative
grade assessment are part of the lecture notes. The test
key can be accessed through my.wisc.edu
- Regrades: Because
partial credit is given the assigned scores reflect a subject
assessment of work done. If you feel that the grader made an error (it
does happen) or the partial credit is inconsistent with your
expectation then please return your exam with a short note stating your
request and why. All regrades will be discussed during the TA meeting
on Friday.
Wednesday, Oct 11 (Chapter 8: Potential Energy, plus Power)
- Link to the lecture, Lecture 11, PowerPoint , Lecture 11 (pdf)
- Almost everyone gave the correct answer to the ball drop path
exercise. That is great(!) because historically this concept
problem often gives students difficulty.
- Regrades: There is a deadline of Monday, Oct. 16 for requesting a regrade.
- I didn't get to either the loop-the-loop demo or the pendulum but I will on Monday.
Friday, Oct 13
Monday, Oct 16 (Chapter 9: Linear Momentum and Collisions)
- Solution to class
problem: Loop-the-loop
- Link to the lecture, Lecture 12, PowerPoint , Lecture 12 (pdf) , Up to exercise 4
- We will finish impulse and center of mass on Wednesday
- Regrades: Today is the deadline for requesting a regrade.
- A revised tutor list is now available, please stop by my office to get one
- Alternative problems to hand in : Ch 7-32 or Ch 8-10.
- HW #5, Ch. 9: 4, 19a,b, 31, 41, 64, Ch. 10, 7, 19a,b, 20, 31, 33, 71 (and one more is likely in the next set)
- Momentum is yet another way of casting Newton's Laws in which a
collision occurs. Momentum is a vector quantity and so we must consider
the vector component individually.
Wednesday, Oct 18 (Chapter 10: Rotation)
- Link to the lecture, Lecture 13, PowerPoint , Lecture 13 (pdf) , Up through rotational inertia.
- Center of mass and rotational inertia are just specialized
perspectives for dealing with Newton's Law of motion. In the case
of center of mass the issue is that no matter how complicated a system
is the center of mass reflects the momentum transfer to an object as a
result of an external force. If no external force then the
velocity of the center of mass remains a constant of the motion.
- In the case of rotational motion around an explicit axis the
rotational inertial plays the same role as the mass in linear motion.
Objects with large rotational moments of inertia are more
difficult to spin (i.e., accelerate angularly) than those with small
moments of inertia. There are important differences. The
center mass may be specified by the mass distribution but the
resistance (i.e., inertia) to linear acceleration doesn't depend on
this distribution. For rotational motion we must specify the
axis of rotation and mass which is father away from the axis exhibits a
stronger inertia to being spun that mass that is closer to the axis of
rotation.
- FYI: A more difficult problem involving Work, Energy and Rotation: Rotating
table-top
Friday, Oct 20
Monday, Oct 23 (Chapter 10: Finish, Chapter 11: Rolling Motion and Cross product)
- Link to the lecture, Lecture 14, PowerPoint , Lecture 14 (pdf) , Up to cross products
- The homework will not dwell on the motion of a top nor
quantization of angular momentum in quantum systems. Still I
encourage you to read through Chapter 11.
- Chapters 11 and 12 are rather modest in length.
- The second midterm will be on Thursday evening of next week.
- HW #6 is available on WebAssign. There are some changes
from the syllabus: Ch 10-79, Ch 11-17,23,30,35,44abdef Ch
12-4,9,21,32,35
- Solution to class
problem: Yoyo
Wednesday, Oct 25 (Chapter 11: Angular
Momentum, Chapter 12: Static Equilibrium
and Elasticity)
- Link to the lecture, Lecture 15, PowerPoint , Lecture 15 (pdf)
- The second midterm will be at 7:15 PM, Thursday of next week, Room, TBA
- Key points: If there is no net external force on system then
linear momentum is conserved. If there is no net external torque
then angular is conserved. Question: Can you imagine a case
where linear momentum is conserved and angular momentum is not?
Friday, Oct 27
Monday, Oct 30 (Catch-up Lecture, Chapter 12: Static Equilibrium
and Elasticity)
- Link to the lecture, Lecture 16, PowerPoint , Lecture 16 (pdf)
- Midterm I in Rm. 105 and 113 in Psychology, McBurney students go to Rm. 5310 Chamberlin Hall (on Thursday, Nov. 2)
- Exam lasts from 7:15 PM to 8:45 PM.
Bring a basic scientific calculator and an 8.5 x 11
in sheet of notes. We can provide blank paper for scratch work
but only work on the exam sheets itself will be graded.
- Most students are really most interested in getting ready for the
midterm. To this end a supplemental set (Ch. 11 and Ch. 12) with
four problems is available. Because time is short (!) I want to
minimize the long hours and so the "exchange" is one for one. The
deadline on the supplemental set is noon on Wednesday. In
addition only parts a and b are required for the loop-the-loop problem
and parts a,b and d for the draw bridge problem. Hint: At the
angle given the draw bridge should fall faster that the horse.
Check the linear acceleration of the point under the horse.
- An important point is that friction is a tangential force
and will always provide a torque. This is true of both static and
kinetic friction.
Wednesday, Nov 1 (Review)
- Link to the lecture, Lecture 17, PowerPoint , Lecture 17 (pdf)
- Midterm I in Rm. 105 and 113 in Psychology, McBurney students go to Rm. 5310 Chamberlin Hall (on Thursday, Nov. 2)
- The exam lasts from 7:15 PM to 8:45 PM.
Bring a basic scientific calculator and an 8.5 x 11
in sheet of notes. We can provide blank paper for scratch work
but only work on the exam sheets itself will be graded.
- Reminder: November 3rd is the last day for dropping a
class, if you have major concerns then contact your TA first and then
me. On a very limited number of cases we can give an estimate of your mid-term grade before 3 PM.
- Main points: If no net external force, momentum is
conserved. If no net external torque, angular momentum is
conserved. This is true piecewise in the x, y and z directions.
The equations look simple but the physics is not. Thus if
there is a net external force then a system will accelerate. If
there is a net external torque then a system will have angular
accelerations. A single force can be the source of acceleration
and angular acceleration.
- Integrals: It turns out there is one small "integral" on
the exam. If you know the equation for the area of a triangle
then this integral can be done without having to mechanically go
through the process of integration. (It is similar to a few of
the prior homework problems.)
Friday, Nov 3
Monday, Nov 6 (Chapter 14: Fluid Mechanics)
- Link to the lecture, Lecture 18, PowerPoint , Lecture 18 (pdf)
- MidTerm 2 is graded: Mean 58.4, Median 58, St. Dev. 16
- Given the level of difficulty the class did much better than I
was expecting. The material was much harder and the exam itself
was more difficult than the first mid-term. You are expected to
cover a lot of material and, given the good results of the first exam,
I became too ambitious and raised the bar a bit too high. Even though
the the average dropped a somewhat I am pleased to see so many students
working so hard. Rotational motion is a very difficult subject.
- The tentative (conservative) curve is on the first page of the lecture note. My thought is that ~30 and above
represents a clear passing grade. Low exam scores (ca. 25-30) can
be mitigated to a large extent with evidence of good
discussion/lab/homework performance. If you continue to work
through the material, you can expect to pass. Perhaps it
may be possible to improve as there are still two exams to go and the
rest of the course is somewhat less difficult.
- The key to solving buoyancy problems is to alway reference the
volume of the fluid displaced. Using that as fixed point will get
you the buoyant force or the work done in a force amplifier.
- HW#7 Ch. 14: 2,8,20,30,52a,54 Ch. 11,19,36,41,49 Honors: Ch. 14: 58
- Regrades: The deadline for requesting regrades is Tuesday, Nov. 14.
Wednesday, Nov 8 (Chapter 15: Oscillatory Motion, Start)
- Link to the lecture, Lecture 19, PowerPoint , Lecture 19 (pdf)
- Regrades: There were, in retrospect, a few additional anomalies
in the exam questions and these need to be addressed. Please hand
in your exam to your TA as soon as possible. The deadline for
requesting regrades is Tuesday, Nov. 14.
- Oscillatory Motion, especially simple harmonic motion, is a
common phenomenon for systems with a linear restoring force (i.e.,
Hooke's Law).
Friday, Nov 10
Monday, Nov 13 (Chapter 16: Wave Motion)
- Link to the lecture, Lecture 20, PowerPoint , Lecture 20 (pdf)
- Regrades: The deadline for requesting regrades is now Thursday, Nov. 16.
- Mid-term 3, yes it isn't too soon to start thinking about the
third midterm exam. To keep in sync with the course material I
have decided to give the exam on Tuesday evening, November 28.
Please contact me before the Thanksgiving holiday if you can't
attend. The exam covers material from chapters 14 through 18.
Thereafter there is just four more chapters to go.
- Homework #8, There have been a few changes, Ch. 16: 3, 18, 30, 40, 58, 59 Ch. 17: 3,15, 34, 38, 40
- Note that the next homework (#9) set includes just one chapter.
Wednesday, Nov 15 (Ch. 16 Finish and Ch. 17: Sound Waves (almost))
- Link to the lecture, Lecture 21, PowerPoint , Lecture 21 (pdf)
- Regrades: The deadline for requesting regrades is tomorrow Thursday, Nov. 16.
- Mid-term 3,To keep in sync with the course material the third exam will be on Tuesday evening, November 28.
Please contact me before the Thanksgiving holiday if you can't
attend. The exam mostly covers material from chapters 14 through 18.
- The traveling wave equation is an extension of simple harmonic
motion. The basic expression is (of course) y(x,t) = A cos(k x -
omega t + phi). In class I let phi be zero for simplicity.
On the first homework problem you won't be able to do this.
This is a wave that varies in space and time with the velocity of energy flow given by v = lambda/ T = omega / k . Notice that there are two velocities that must be reconciled,
that of the energy flow and that of the mass element situated at a
point on the string. Thus you must consider independently two
facets of the wave. At fixed position and at fixed time.
Now x, y and t must reconciled and hence wave motion is more
difficult than SHM (simple harmonic motion).
- At fixed t: Let t=0 and so now we have y(x,0) = A
cos(kx + phi) and this will give the displacement of the string every
in space.
- At fixed x: Let x=0 and so now we have y(0,t) = A cos(-omega t
+phi) and this will give the displacement of a specific piece of the
string with time. We can get its position y if we know t, omega,
A and phi or its velocity from dy/dt = omega A sin(-omega t +phi)
if we know t omega, A and phi. This the "second" velocity and
describes the local motion of the disturbance. For the first homework problem you will need to use this fact.
- NOTE: Problem 2 on the homework. This problem actually references a sine wave (although everything
is set up in the text for a cosine). So now you need to start with
y(x,t) = A sin(-kx - omega t +phi ) or A sin(kx+ omega t + phi). Of
these WebAssign wants you to choose the later. These multi value
solutions can be problematic.
Friday, Nov 17
Monday, Nov 20
(Ch. 17: Sound)
- Link to the lecture, Lecture 22, PowerPoint , Lecture 22 (pdf)
- Mid-term 3,To keep in sync with the course material the third exam will be on Tuesday evening, November 28.
Please contact me before the Thanksgiving holiday if you can't
attend. The exam mostly covers material from chapters 14 through 17 (plus elasticity and moduli).
- This mid-term builds on concepts developed in the first twelve
chapters and so you should remember to copy important formulas from the
first two exams on your note sheet. If you happen to forget to
include one then you are, by all means, welcome to ask the TA
proctoring the exam for assistance.
- Note 1: Even though I will lecture on Chapter 18 on
Wednesday, this material will only appear on the final. Homework set #9
will be lumped together with that of Chapter 19 and due two weeks from
tomorrow.
- Note 2: Monday, Nov. 27 will be a review section for the exam
- Note 3: Homework #8 will be due on Wednesday at noon.
Wednesday, Nov 22 (Catch-up Lecture, Ch. 18: Superposition and Standing Waves)
- Link to the lecture, Lecture 23, PowerPoint , Lecture 23 (pdf)
- The third exam will be on Tuesday evening, November 28 (again in
the Pyschology lecture halls).
The exam mostly covers material from chapters 14 through 17 (plus
elasticity and moduli). McBurney students should go to room 5310
in Chamberlin Hall.
- This mid-term builds on concepts developed in the first twelve
chapters and so you should remember to copy important formulas from the
first two exams on your note sheet. If you happen to forget to
include one then you are, by all means, welcome to ask the TA
proctoring the exam for assistance.
- Monday, Nov. 27 will be a review section for the exam
Happy Thanksgiving!!!
Monday, Nov 27 (Review)
- Link to the lecture, Lecture 24, PowerPoint , Lecture 24 (pdf)
- The third exam will be on Tuesday evening at 7:15 PM on November 28 (again in
the Pyschology lecture halls).
The exam mostly covers material from chapters 14 through 17 (plus
elasticity and moduli). McBurney students should go to room 5310
in Chamberlin Hall.
- In the class I noted that there are parallels between the natural resonant
angular frequency in torsional motion for a physical pendulum or a
torsional pendulum whether the force is due is to gravity or a Hooke's
Law spring. In all cases omega^2 is proportional to something
torque like in the numerator and rotational inertia like in the
denominator. Of course the actual numerical values are example
specific.
Wednesday, Nov. 29 (Chapter 19: Temperature)
- Link to the lecture, Lecture 25, PowerPoint , Lecture 25 (pdf)
- Temperature is ubiquitous in our daily lives but its actual
physical meaning is difficult to discern. For example if you
touch a 0 C piece of metal or a 0 C piece of cloth you might be
inclined to say that the metal feels colder even though they are really
at the same temperature. Here you are prejudiced by the heat
flow. In thermodynamics temperature
is the property of a system which tells you the net direction that heat
will flow if two objects are brought into thermal contact (i.e., heat
transfer is possible). Heat flows from high temperature
objects towards low temperature objects. At thermal equilibrium
between two objects there will be no net heat flow and the objects will
be said to be at the same temperature.
- This said we now note that temperature can be related to the
internal energy of a system. Generally as materials cool from
high temperature to low temperature the internal motions of the
constituents decrease. After one defines temperature reference
standards, i.e. the boiling point of water at a specific pressure and
the triple point of water, then one can deduce a temperature at which
all classical internal energy will go to zero. The point is called
absolute zero. At absolute zero all motion does not cease because
of the nature of quantum mechanics. At low temperatures many
materials show new striking behavior resulting from quantum properties
(i.e., superconductivity).
- NOTE: Because of a committee assignment I will not be able
to hold my usual office hours on Monday. Please contact me by
e-mail and I will do my best to meet with you after 5 PM on
Monday.
Friday, Dec. 1
Monday, Dec 4 (Chapter 20: Heat and 1st Law of
Thermodynamics)
Wednesday, Dec 6 (Chapter 21: The Kinetic Theory of Gases)
- Link to the lecture, Lecture 27, PowerPoint , Lecture 27 (pdf)
- Although I have stressed the importance of temperature as an
indicator for determining heat flow (a process) there are addition
relationships between the internal energy of a system and temperature.
Here we are told that classically, for each "degree of freedom",
there is a factor of 1/2 k_B T in internal energy per particle.
For a monoatomic classical gas the x, y and z motions can be
individually added R(vector) = x i(unit vector) + y j(unit vector) + z
k(unit vector) with a resulting energy of 1/2 m (v_x^2+v_y^2+v_z^2)
(i.e., three independently added terms) so that the total internal
energy per particle is 3/2 k_B T.
- However one must be careful with respect to the breakdown of
classical physics. At low temperatures the number of energy
levels accessible becomes comparable to the number of particles.
Thus we can measure deviations from the classical result of the
equipartition theorem.
- The generalization to other more complicated working "fluids" is
straightforward. In a diatomic gas, i.e. N2, O2, the dumbbell
shaped object has two rotational degrees of freedom and one internal
vibrational (i.e., a stiff interatomic spring constant). On
heating the accessible degrees of freedom stepwise increases from 3 to 5
(rotation) to 7 (spring potential energy and kinetic energy). The
internal energy reflects this as well as the heat capacity.
- We also introduced cyclic processes which allow one to extract
useful work from an "engine" through energy transfer. Although
this is developed in regards to heat and two thermal reservoirs at
different temperatures the underlying principles are universal.
- Student evaluations will be administered on Dec. 13.
- NOTE 1: There is a room change for the final. The room will be announced next week.
- NOTE 2: Before lab this we you will be given the same
exercise that you received during the first day of discussion.
Our goal is to establish a series of metrics to assess learning
and improve the delivery of the introductory classes. We really
appreciate you assistance in this study!
Friday, Dec 5
Monday, Dec 11 (Chapter 22 : Second Law
of Thermodynamics)
- Link to the lecture, Lecture 28, PowerPoint , Lecture 28 (pdf)
- Student evaluations will be administered on Dec. 13.
- NOTE: Room assignment for final, the Physics 207 Final exam is on Dec. 19 at 2:45 pm in Rooms B130 Van Vleck
and B102 Van Vleck. McBurney student tentative room assignment: 5310
Chamberlin Hall. If all goes well we should have grades available
by Thursday evening.
- NOTE 2: Before lab this week you will be given the same exercise set that
you received during the first day of discussion. Our goal is to
establish a series of metrics to assess learning and improve the
delivery of the introductory classes. We really appreciate your assistance in this process.
- Today we just started talking about the efficiency of
thermodynamic cycles and the 2nd Law of Thermodynamics. On Wednesday we
will finish.
- Friday there will be a review session for the final
- Homework 10, 2nd problem (the lead bullets): There seems to
be a snafu with the WebAssign answer key. Please wait until I
hear from the WebAssign people that the problem has been fixed.
My apologies if this caused frustration.
- Homework 11 is now accessible. Chapter 22 problems: 6,7,17,37,46
Wednesday, Dec. 13 (Catch up and Review for Final)
- Link to the lecture, Lecture 29, PowerPoint , Lecture 29 (pdf)
- NOTE: Room assignment for final, the Physics 207 Final exam is on Dec. 19 at 2:45 pm in Rooms B130 Van Vleck
and B102 Van Vleck. McBurney student tentative room assignment: 5310
Chamberlin Hall. If all goes well we should have grades available
by Thursday evening.
- Today I talked about reversible and irrevsible processes.
In a reversible adiabatic expansion (Q=0) we would expect the
change in entropy to be zero. There is a two term formula
given in class (derived in Serway and in the lecture notes) that
reflects the change in entropy for the volume change (up) and the
temperature change (down). As "anticipated" the sum of these two terms
is indeed zero. This is explicitly done in the lecture notes
(but, as far as I can tell, not in Serway). Therefore, in the
Carnot cycle, any net change in the entropy occurs during the two
isothermal steps. These must be equal in magnitude and opposite
in sign because entropy is a state variable. Thus in a full cycle,
S_initial = S_final, and so any net change in entropy of the system
(here engine plus reservoirs) reflects the heat transfer between the
reserviors. In the perfect Carnot cycle there will be a drop in
the entropy of the high temperature reservoir and an increase in that
of the low temperature reservoir. With the perfectly reversible
Carnot cycle these too are equal and opposite. Example: 200
K and 100 K with 100 J of heat transfer out of the 200 K reservoir.
Efficiency is 0.50 so 50 J of work and 50 J of heat transfer goes
into the 100 K reservoir. Delta_S= -100 J/200 K + 50 J/100 K =0.
The Carnot cycle is the best you can do without violating either
the first or second laws of thermdynamics!
- Friday there will be a review session for the final
- Chapter 22 problems: 6,7,17,37,46. Due Friday at midnight.
- Biocore students, please contact me if you are concerned about back to back exams.
Friday, Dec 15 (Review for Final)
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